I'm starting a study about theory of transformation groups and equivariant cohomology, in what I read several times that Čech cohomology is the most compatible with this theory, but until now I haven't found an explanation for that. I suspect that it has to do with finitistic spaces (or perhaps vice versa), but I am not certain. Can someone explain to me the real reason for that, please?
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2$\begingroup$ The fixed point set of a compact Lie group action on a manifold is often a complicated subset, and the singular cohomology cannot pick up its features or how it sits in the ambient manifold. $\endgroup$– Igor BelegradekCommented Feb 27 at 14:02
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One reason is that it is easier to make equivariant open coverings of $G$-spaces than to make equivariant triangulations of $G$-spaces.
(I was going to add this as a comment but saw the script warning me to avoid answering questions in comments. So it's a too brief answer instead.)
